 There are two ways to do it. One is we can define our capacity as our normal rate of output defined as normal rate of output. When I say normal rate of output, what we mean is that if this is a speed at which we typically work, you can take that as that capacity. So, if suppose the pressure is higher, we are able to do little more also, we are able to work little faster. So, we can define our capacity as a normal rate of output. So, if my schedule pressure becomes very large, then I am able to produce or work faster and produce little more than what I do normally, ok. So, in this case, what is it? Capacity utilization must pass through 1 comma 1, yeah, must pass through 1 comma 1. That means, it is not saturating it to 1 comma 1, we are able to produce at a slightly higher than what is the capacity. When you ask what is the capacity, they may say, ok. Capacity is to produce a 50 burgers in 1 hour, let us say 100 burgers in 1 hour. But if there is lot of pressure, they may be able to produce 110 burgers or 120 burgers. So, suddenly it does it sounds like as if they are producing more than their capacity. In fact, they are not. When they define capacity as normal rate, normally what can you do? It can do 100. But if really if I have to, there is lot of pressure, lot of orders, yeah, we can speed things up, we can cut the brakes, we can make it little more better, I can produce little more, maybe 100, 20, 100, 25 whatever, some slightly larger number, right. So, that is what we mean define the capacity as here. So, here if, so that is mean when schedule pressure is 1, then shipment must equal your desired production, must equal your capacity. So, this will be your reference point, right. So, when schedule pressure is just 1, that means if this is a normal rate of output is 100 and if demand is also 100, I must be able to achieve it. If it is something more, I can whatever put in little more effort and be able to achieve little more, then that is also. So, that is what is defining here. So, this is one approach, right. This is one way, but we can also define alternatively also. Alternately, we can define the capacity as a maximum possible output. Alternately, capacity defined as max possible output. This implies that capacity utilization is less than 1 in normal scenarios, right. Then your schedule pressure we defined as desired production divided by normal capacity utilization multiplied by your capacity. Then utilization will pass through the reference point 1 comma normal capacity utilization and saturate at 1. Take it carefully. So, here what you are saying is suppose you define capacity as the maximum possible output, this maximum burgers I can ever produce, right. That means your reference point cannot pass at one commandment. Schedule pressure is there regularly how much can you make. So, that will be much lower than that actual capacity we are defining and the maximum saturation will occur at value 1, ok. So, we will take this one. What is written blue? We will do it for this one. So, the capacity let us define as a normal rate of output. So, that means capacity utilization must pass through 1 comma 1 that it means when schedule pressure is 1 that means I must be able to produce it. So, schedule pressure is more than 1 that means I may be able to produce little more than what we can do or what is defined normal capacity. Next, we have to define some reference policies, right. So, let us go ahead and do that. Let us define some reference policies. Your schedule pressure and capacity utilization is your reference policies, right. Both are dimensionless this is what we have. Now, we can define some reference lines. Let us define one line. When shipment is equal to the capacity then what should be the line? C u should be 1. When shipment is equal to capacity, C u should be 1. So, let us just take that. Let us put that as 1 and let us draw a straight line. So, in this straight line C u is equal to 1 and this corresponds to the policy that shipment equal to capacity, right. So, this is line A that we have. What else policy can we have? What if I am able to ship all the whatever the desired production I am able to make it, right. What will be that line? Whatever the desired production I am able to ship it. That means shipment is equal to desired production, right. That must be must be a 45 degree line. So, let us go ahead and draw a 45 degree line. I hope it looks 45 degrees, but yeah go with it. So, this case C u is equal to the schedule pressure, right. If capacity utilization equal to schedule pressure that means whatever I am is my demand I am able to keep shipping that same amount. So, let us this be curve B, curve A. Now comes the more interesting lines. What else could be the reference policies here? When we do many models we typically assume this saying that if schedule pressure is less than capacity then do schedule pressure or do capacity. I can use a wind or max function and just simply model it, correct or if then else construct we saw it last time. But in this case we want to make it more realistic saying that you do not get exact such shifts as we approach closer to the full capacity I may not be able to produce at the same speed 1. And 2 if order is very less I am able to get it even faster because I am at a very low capacity, right. So, suppose my schedule pressure was hardly anything. So, I may be able to do it things much faster than what it is, right. So, how much faster can I go? Suppose my schedule pressure is low that means my demand is very low as compared to capacity. Capacity is say 100 my demand is say for 10, right. So, I will be somewhere here. So, in that case how much early can I go? How much sooner can I finish it, right. So, I must be able to do it much faster, right. So, there the utilization could be much higher. But I can only go to up to some limit. There has to be some processing delay. There has to be some heating delay or some processing delay. I cannot speed up much lower than that particular value. So, for now just bear with me. So, let us draw one more line called, let us call this line Cu is equal to S max multiplied by S p. Let us call this curve C. Let us see what it means. Let us do only for curve C. Curve A and B is kind of obvious. So, we are just going for curve C. So, the line Cu is equal to S max multiplied by S p where S max is the maximum slope of function. It will it corresponds to policy of, corresponds to policy of producing and delivering as fast as possible. As fast as possible means minimum delivery delay. Just read it once. So, what you are saying is when the demand is only 10 and when capacity is 100, then I can actually work much faster and produce things at a much higher rate. Though the target delivery delay may be 1 v, I am able to deliver it within 4 days. I may not be able to deliver it in 1 day. Maybe it takes some time to actually produce it, but I may not need to wait until the fifth day or sixth day to deliver it. I may deliver it much faster, but there is some limit S max. I do not know what it is, but it is some limit. Let us see, go ahead and try to find out how to derive this S max. So, let us try to compute for curve C. So, C itself, we are continuing that. Let us go to our basic equations. Shipments is defined as capacity into capacity utilization, correct. So, now, on that curve C, it is nothing but C into S max into schedule pressure, which is C into S max. What is schedule pressure? Schedule pressure is nothing but desired production divided by capacity, which means it is S max times my desired production. What is desired production? Back log divided by target delivery delay D star. So, recall your, so suppose this is your shipments, what is this represent? This represents the max possible shipment rate, correct. Now, if you recall the delivery delay equation, so let us then call it shipments star say. So, this delivery delay was defined as back log divided by shipments, correct. So, suppose then to get the minimum delivery delay, I can substitute B by shipment star, which is nothing but B by S max into B by D D star, which is nothing but desired delivery delay by S max or S max is nothing but your D D star divided by D D min. So, you can compute the slope because you know both the parameters. D D star is a reference delivery delay. What the company is promising? This is the delivery delay I am promising. It will take a week to produce. D D min is, you know what is the minimum time it is going to take? What is the minimum total cycle time it is going to take to produce? There is absolutely no delays. So, that we cannot go lower than that. There are physical limits to it. So, based on that we can define that is the maximum speed at which I can ever ever produce, push comes to show that is the maximum I can ever do. It can easily be computed and we can get those values or let us go back to the sheet. So, now we have three values. Can you come up with one more curve? Suppose my schedule production is much higher than my or my desired production is much higher than my capacity. So, that means the value here. So, this is SP and this thing. So, this point has to be 1, but can I keep on producing on this line B forever? No right. I cannot keep on producing on this line or even this line forever. So, I need to saturate at some point. Let us for modeling sake let us simply define another line say Cu is equal to Cu max. Let us call it line D. It is possible reality also to get your Cu max because the maximum utilization ever possible. So, physical limits you know this is the maximum over time people convert. This is the maximum people I can employ even if there is physical the machines can only work for so much time. So, based on that you can say how much maximum you can produce even if you can produce a normal rate 100. If the order is for 10,000 units you clearly cannot make it. Maybe you can go up to 110 or 120 or 25, run on 30, 150 whatever. So, that is a maximum you can never do right. Somewhere it will saturate right. So, now we have these nice reference policies ok. Now, step 4 in our list of steps or guidelines you are supposed to find out what is the what happens under extreme conditions. What happens in schedule pressure is 0? It has to be 0. So, one extreme condition can backlog be negative you can say that does not occur in this particular scenario. So, that should not occurs anything less than 0 I should not be able to ship anything right. So, if that means schedule shipment has to be 0. If no orders come in backlog has to be 0, desired pressure has to be 0 that means shipment has to be 0. And when schedule pressure is very large or desired production is very large that means it is saturated C max. So, at some value here it should reach C max. So, only two possible limiting conditions you have anything 0 or lesser it should be 0. Anything more than at a large value C max, C u will take only a maximum value of C max whatever be the value up to infinity suppose it has to take C max. So, that is the extreme condition that we have thought. And domain we can maybe quickly I will write it here. So, domain SP has to be between 0 to plus infinity it can go there, but capacity utilization typically between 0 to C u max that is the domain of the variable we need to ensure that this is what happens. So, we have defined that. Now, is the fun. Now, we need to define. So, we need to define some possible shapes for the curves that is what kind of because we are not drawn that the idea of this is to figure out what is the shape of the curve that we are interested in. But before doing that can identify the feasible and infeasible regions here naturally because of various lines we are getting various zones and regions. One obvious is anything above this line is infeasible right. So, I do not need to bother about that. So, let me just put a infeasible, infeasible, infeasible area see you can never take any values beyond that. So, that is gone. What about this region here? Why not? Because it is to left of S max. So, I can never produce it. So, this also becomes my infeasible region infeasible region. What about this? It is possible it is feasible because I am going to get this between S max and the regular capacity utilization. So, we are going to assume that people do not work much more slower than they have to and suppose we target this one week and there is no pressure we hope it will finish in one week it does not get unnecessarily delayed. So, this is fine. So, this region also company will not like to operate here meaning there is no schedule pressure you are going lesser than that deliberately. So, this also is infeasible. What about this region and this region? Feasible or infeasible? What about this? What about this? Not feasible? Anyone else? Ok, we will come to that. See what are the other reference point that we had? The curve passes through 1 comma 1. This was a reference point. Curve passes through 1 comma 1. It can certainly not pass from here, right? Then curve has to come from in this zone and pass through here. Then it has to do some real gymnastics if it has to jump here before it will be like some here and then goes up like that. If it is going to pass through 1 comma 1 that means as I approach this capacity I am unable to work at this S max space or I am unable to work at the minimum delay because I need to take time, right? Because normal capacity I am using my target delivery delay. So, if anything is going beyond that my pressure is going beyond that then my delivery delay will get delayed. My total delay will be more than the target. That means I cannot go faster than my schedule pressure because that itself maintaining itself is difficult. So, maintaining a region earlier than that is going to even more difficult or not possible at all. So, in that sense this region also became infeasible. So, now I am left with only two domains here where it can be feasible, right? So, logic dictates that at low values I may be operate up to S max. So, let us just arbitrarily put a blue should I I will try red again. It is easier to see. Maybe up to a point I can operate at the S max, right? Beyond that it is very difficult to maintain the minimum delay because natural delay is more orders come in then I cannot operate a very minimum delay then I start moving away from that. Then I pass through 1 and then I keep going and saturate at some particular point. So, this can be a typical curve that we cannot play with. Let us then try to understand the physics or the reality behind these two lines here. These are the key lines that is here. So, this is when I am operating at the schedule pressure at the regular delay. This when I do not have much work then I can operate very fast. I can achieve the minimum delay. Suppose it takes average of 1 week to do things, if I am operating here that means I am going to finish the job in 4 days, right? As more and more work comes in it is going to be very difficult to maintain that 4 days delay because I am only promising people 1 week. So, I am going to start working only at that 1 week delay time. So, as my schedule pressure goes higher or my desired production or the backlog becomes larger, right? When schedule pressure becomes higher means what? Design production means it goes higher which means backlog should have gone higher. Everything else are constant. So, as backlog becomes larger I cannot work at this minimum delay. So, we have to work at this at a standard, this is a schedule pressure as a normal capacity I am able to produce a 100 burgers, let me produce that because order is 100 I can produce 100. That is the speed at which and it will take so much time. So, I work out that much amount of time to achieve that. Yes, whether we stop very early at 10 percent, 20 percent, 30 percent that depends on our speed and the actual region. So, you can actually come like this and what you are saying is it can go much tangentially and it can saturate flatter or it can go very steep and saturate much quicker to that or it can take much longer time to saturate. So, all those so within this feasible region we can have many infinitely many combinations of curves, but we are not going to get a different shape of the curve. The shape continues to remain the same, that is the idea. So, at this point we have to make some assumptions so that we can enter the values and start building the model. Suppose we say our normal capacity is 80 percent of the maximum capacity ok. So, then if capacity utilization is 1, then C max will be about 1.25 right. Normal capacity is 80 percent of the maximum ever possible, then the max is possible and then you define that 80 percent as 1 that means, capacity max has to become 1.25. The simple numbers we can have and then we can divide it into different intervals to identify and draw what is the curves that we want. So, let me just go back to our slides. So, these are the steps we did. We did normalization, we identified reference points, reference policies, X-ting condition, domain, possible shapes, we have drawn, we have drawn one shape. Now, we need to specify the values of the function. That is up to us how long we want to do it to saturate it. I have entered one such combination in our winsome. Let us just quickly see that model. Since we know how to enter the table function, we can just directly see that function non-linear. So, model I am not sure this is the final one. Schedule pressure is defined, capacity utilization as graph ok. So, here you can observe the input. Schedule pressure goes increments of 0.25 and goes all the way to 2.5 and the output goes from 0.33, 0.62, 0.85, 1. These are just some arbitrary numbers that has been put. But idea is it saturates at a max value of 1.25. We put to some extra value so that if schedule pressure goes beyond 2.5 also, it has to be C max has to be 1.25 that is the character is taken. One extra few redundant values are also there to ensure that the curve actually flattens out at that particular capacity utilization. How we know it is operating S max? It is because a normal input is 25, but here it is 33 percent is output. So, you are operating at a higher speed than you are able to work on it. At 1 come on it means at 0.25 you are operating at slightly higher than that, 0.5 you are operating slightly higher even 0.7 you are operating slightly higher only then you cut into 1. After that you are operating at a lower speed 1.25 or operating at only 1.1 110 percent of your capacity though your pressure is to work at 125 percent. When pressure becomes 1.5 still it goes only little more little more etcetera and then saturates. So, these values are closer to your S max and here it cuts your 1 comma 1 point starts at 0 0 and then it saturates at 1.25. So, if you simulate it I am not even sure what is order equation looks like we are going some step input function we can visualize it. These are orders that has come based on the orders this is a schedule pressure that has occurred sometimes it goes beyond 1.5 then sometimes it goes close to 0.6 you can see both together. You can see the capacity utilization the red line starts at 1 and then goes up to 1.2 and then again falls down to 0.8 and fluctuates there where schedule pressure goes all the way to 1 point more than 1.6 then falls much below. When schedule pressure falls below still I am capacity utilization 0.8 I am able to work faster. So, I am operating not on that line a little away from the line closer to S max X max. If you model delivery delay against the target delivery delay consider target delivery always 1 which is one week which was given. When the schedule pressure was high when orders was more in that time my average delay increased, but then average delay then fell down I am able to produce much faster. So, this we are approaching the minimum delivery delay the right here. So, building the model we observed how schedule change capacity utilization changed for schedule pressure how the orders affected change in schedule pressure what are the ranges etcetera which is so. These are the steps that we did how do you normalize reference points and the extreme conditions we checked we draw the functions and did a test graph. You can do sensitivity analysis to figure out where is the maximum capacity utilization sensitivity 1.2 to 1.5 vary the minimum delivery delay from half of target to other extreme where it equals target. Here minimum delivery delay you have to figure out S max right. So, we can change suppose X max suppose the minimum delivery delay could be just half a week then what happens then you can vary the slope at their operating point. The base case slope is 0.6 at the operating point, but you can try to change it more flatter or more steeper to see how it fluctuates your production rate is going to flow shipment rate fluctuates based on the shape of the curve. And then you can try to work on this question base case flat and steep case will schedule pressure be high. So, you can try to I will I will upload some of the sample models you can take a look at it and run it. Thank you.